Moreover, a scalable HOEVD solver, \(\textsc {s-hoevd}\)  in line 1 of algorithm, is utilized for good initialization; see subsec: scalable HOEVD for details.
We also use AdaGrad [1]} to automatically tune step sizes.
Specifically, we implement the column-wise extension of AdaGrad proposed in [2]}, since it is natural to independently update the orthonormal basis vectors in \(\mathbf {Q}\) . See lines 4 and 5, where \(. \slash \)  is the columnwise division.
